We have related the diagonal and off-diagonal elements of the effective self-diffusion tensor, D, to the echo intensity in NMR spin-echo experiments. Using this expression, we have designed pulse sequences from which we can estimate D using a series of diffusion-weighted images. This estimate is validated using isotropic and anisotropic media. One application of this work is to use D to determine fiber orientation noninvasively in vivo. Moreover, we can infer mean diffusion distances and tissue microstructure within a voxel. We also have developed a new MR imaging modality: Diffusion Tensor MRI, in which we use D to construct images of diffusion ellipsoids that depict the local fiber orientation and mean diffusion distances, as well as images of the three scalar invariants of D that are independent of the reference frame in which magnetic field gradients and D are measured, and to provide new information about tissue microstructure and physiology. Clinical applications are anticipated in stroke monitoring and tumor diagnosis.